The energetics of rapid cellular mechanotransduction

Significance The rapid transduction of mechanical forces is crucial to our senses of touch and proprioception in addition to regulating homeostatic processes such as blood pressure and bone density. This work combines atomic force microscopy and electrophysiology to provide a perspective toward quantifying how cells function and specialize as sensors of mechanical energy, which is a prerequisite for understanding how stimulus intensity and dynamics are decoded.

Cells throughout the human body detect mechanical forces. While it is known that the rapid (millisecond) detection of mechanical forces is mediated by force-gated ion channels, a detailed quantitative understanding of cells as sensors of mechanical energy is still lacking. Here, we combine atomic force microscopy with patch-clamp electrophysiology to determine the physical limits of cells expressing the force-gated ion channels (FGICs) Piezo1, Piezo2, TREK1, and TRAAK. We find that, depending on the ion channel expressed, cells can function either as proportional or nonlinear transducers of mechanical energy and detect mechanical energies as little as ~100 fJ, with a resolution of up to ~1 fJ. These specific energetic values depend on cell size, channel density, and cytoskeletal architecture. We also make the surprising discovery that cells can transduce forces either nearly instantaneously (<1 ms) or with a substantial time delay (~10 ms). Using a chimeric experimental approach and simulations, we show how such delays can emerge from channel-intrinsic properties and the slow diffusion of tension in the membrane. Overall, our experiments reveal the capabilities and limits of cellular mechanosensing and provide insights into molecular mechanisms that different cell types may employ to specialize for their distinct physiological roles.

force-gated ion channel | mechanotransduction | mechanotransmission
The ability to detect mechanical forces is essential for a breadth of physiological processes including our sense of light touch, proprioception, blood pressure regulation, bone homeostasis, interoception, and cell differentiation (1)(2)(3)(4)(5)(6)(7). Despite this broad importance, our quantitative understanding of cells as sensors of mechanical energy is extremely limited and even seemingly simple questions about cellular mechanotransduction remain unanswered: What is the smallest mechanical energy a cell can detect? What is the smallest mechanical energy a cell can resolve? And how fast can cells respond?
The most rapid detection of forces is mediated by force-gated ion channels (FGICs), which respond in as little as 40 µs by gating the flux of ions (8). FGICs vary in their ion selectivity, single-channel conductance, and gating kinetics, which enables cells to transduce mechanical forces into distinct electrochemical signals. However, how FGICs compare in their most fundamental property, the sensing of mechanical energy, is not well understood (9). For example, measurements of the gating energy of the well-studied ion channel Piezo1 differ substantially (8 × 10 −21 J and 40 × 10 −21 J), while for the two-pore domain potassium (K2P) channels TREK1 and TRAAK, estimates span 1 to 10 × 10 −21 J, and for Piezo2 and the recently discovered TMEM63 channels, such information is missing altogether (10)(11)(12)(13)(14). Similarly, fundamental molecular mechanisms of many FGICs are still unclear: While some FGICs, such as Piezo1, TREK1, TREK2, and TRAAK, can be directly activated by membrane tension, others such as NOMPC sense force through tethers (10,11,(15)(16)(17)(18)(19)(20). Importantly, both mechanisms are not mutually exclusive and may act in synergy (21).
Structural and mechanical properties of the cell are tightly coupled to force detection. Specifically, the actin cytoskeleton can absorb mechanical forces (mechanoprotection) while also transmitting forces near or directly to the FGICs (mechanotransmission). For example, the actin cytoskeleton is a major determinant of cell stiffness and slows the transmission of membrane tension (22,23). In contrast, the actin cytoskeleton can tether to Piezo1 via the cadherin-ß-catenin complex so that actin disruption decreases Piezo1mediated responses to cell indentation. Additionally, the actin cytoskeleton has been proposed to transmit long-range forces to Piezo2 channels (24)(25)(26). Effectively, both processes compete and therefore to what extent the actin cytoskeleton facilitates or impedes force sensing remains an open question.
Another impediment to a quantitative understanding of cells as mechanotransducers is technical limitations: The standard assays for probing cellular mechanotransduction use stimulation by pressure clamp (stretch) and cell indentation (poke) in combination with patch-clamp electrophysiology (27,28). While both methods provide an accurate readout of the electrical response, stretch stimulation disrupts the underlying cytoskeleton and does not inform about the overall cellular response, and poke stimulation cannot quantify the magnitude of the applied force. More sophisticated methods for mechanical stimulation include magnetic force actuators, atomic force microscopy (AFM), optical tweezers, and ultrasound but often are combined with calcium imaging, which does not yield a precise measure of channel activity or kinetics and precludes the study of FGICs that do not conduct calcium (29)(30)(31)(32)(33)(34)(35)(36)(37)(38)(39)(40). In summary, none of these assays can stimulate cells with a precisely quantified indentation, force, and energy while also measuring the transduction current with the gold standard of electrophysiology.
Here, we developed an instrument that combines atomic force microscopy with patch-clamp electrophysiology to allow for quantitative mechanical stimulation and simultaneous detection of the evoked transduction current. With this tool, we set out to explore and precisely quantify how single cells convert the energy of mechanical compression into an electric signal.

Simultaneous Measurements of Cell Compression and
Mechanotransduction. To quantify the magnitude of energies that cells can sense and respond to, we built an instrument that combines an atomic force microscope (AFM) with patchclamp electrophysiology ( Fig. 1 A-C). In each experiment, a flexible cantilever compresses a single cultured cell at a speed of 40 µm/s, and then holds its position for 100 ms, before it is retracted at the same speed. We chose this specific speed because it elicits robust mechanotransduction currents while minimizing hydrodynamic drag on the AFM cantilever. The cantilever, whose dimensions are comparable to the size of the cell, is centered on a cell, and displaced for a total of ~6 µm, which altogether results in a large-scale compression of the entire cell. Since the stiffness of each cantilever and the sensitivity of the detector to cantilever bending are calibrated for individual experiments, we can calculate the distance (d), compression force (F), and cumulative work (W) performed on the cell throughout the entire experiment with a relative uncertainty of ≲20%. Additionally, we estimate the cumulative work associated with hydrodynamic drag on the cantilever to be 11.8 ± 2.2 fJ at most (Methods). We stepped the cantilever down into the cell until either a mechanotransduction current was elicited or the patch ruptured. This resulted in the maximum work applied to each cell that ranged from ~170 to 1,300 fJ (SI Appendix, Fig. S1). At the same time, we recorded electrophysiologically from the cell by patching it in the wholecell configuration, which enables us to measure the evoked transduction current (I) (Fig. 1D).
Initial validation experiments on HEK293T cells overexpressing the force-gated ion channel Piezo1 show that AFM compression evokes rapid transduction currents at −80 mV, which are absent in cells transfected with YFP as control. Peak current amplitudes (1.1 ± 0.5 nA, n = 16) are comparable to those from classical poke-indentation experiments and inactivate with a time course of 25 ± 4 ms (n = 16), which is expected for Piezo1 at this holding potential (41,42). We observed that the cantilever deflection undergoes a small but noticeable adaptation during the static phase with a time course of 33 ± 3 ms (n = 16) when fit with a single exponential decay, perhaps due to relaxation of the cell. We therefore focused all subsequent analyses on the approach phase to calculate distance-current (d/I), force-current (F/I), and workcurrent (W/I) relationships for understanding how cell compression evokes mechanotransduction (Fig. 1E). Linearity of Cellular Mechanotransduction. We next performed systematic AFM-electrophysiology experiments on HEK293T cells overexpressing the FGICs Piezo1, Piezo2, TREK1, and TRAAK ( Fig. 2A and SI Appendix, Fig. S2). We first noticed that the W/I relationships differed qualitatively in their linearity: Cells expressing TREK1 and TRAAK showed currents that were approximately proportional to the work performed on the cell. In comparison, the W/I relationships from cells expressing Piezo1 and Piezo2 appeared nonlinear. This qualitative difference suggests that cells may in principle function either as proportional or nonlinear transducers of mechanical energy. For quantification, we fit all individual measurements with a power law ( I = W ), where a power coefficient α = 1 indicates a perfectly linear (directly proportional) transduction of mechanical work into current (Fig. 2B). Consistent with our initial observation, the W/I relationships of cells expressing TREK1 and TRAAK have power coefficients of 1.4 ± 0.1 (n = 60) and 1.9 ± 0.2 (n = 38), respectively, confirming that cells expressing TREK1 and, to a lesser extent, TRAAK behave nearly as proportional transducers of mechanical energy. However, cells expressing Piezo2 and, even more so, cells expressing Piezo1 have substantially larger power coefficients of 2.6 ± 0.2 (n = 47) and 6.2 ± 0.4 (n = 39), respectively, meaning that their responses are indeed highly nonlinear; i.e., their force detection is akin to a switch. More generally, the data demonstrate that the identity of the transduction channel defines this important response property.

Threshold and Resolution for Detecting Mechanical Energy.
To quantify the transduction response further, we next calculated for each individual cell its detection threshold (W threshold ) or the mechanical energy required to elicit a detectable transduction current (Fig. 3A). While measurements vary substantially between individual cells, summary data show that each channel type also confers distinct detection thresholds (Fig. 3B). Cells expressing TREK1 exhibit the lowest thresholds of 68.2 ± 6.3 fJ (n = 60), whereas cells expressing Piezo1 exhibit the highest thresholds of 213.7 ± 16.6 fJ (n = 39). In addition, the detection thresholds of cells with the respectively related channels TRAAK (124.5 ± 11.9 fJ; n = 38) and Piezo2 (86.8 ± 7.1 fJ; n = 47) differed by roughly twofold from their paralogs, meaning that detection thresholds are not conserved within channel families.
Notably, in this analysis, the current amplitude corresponding to W threshold is equivalent to the activation of only ~2 ion channels (see Methods and refs. 43 and 44). Thus, considering that activating two Piezo1 channels requires an energy of ΔG ~80 × 10 −8 fJ (10,11) directly implies that >10 7 times more energy is absorbed by the cell before transduction is initiated. This result shows a considerable capacity of the cell to buffer mechanical energy. We next reasoned that once this initial buffering capacity is depleted, the subsequent activation of FGICs may be more efficient. To test this idea, we quantified the work resolution (W resolution ), which we define as the inverse maximum slope of the W/I relationship normalized by the unitary current of the transduction channel (see Methods and Fig. 3C). Intuitively, this measure can be understood as the minimal mechanical work required to open the very next ion channel or as the smallest mechanical energy a cell can discriminate. Indeed, we found that values for W resolution were almost 100-fold smaller compared to those for W threshold , and in addition, unlike detection thresholds, similar between related ion channels. Specifically, values for W resolution are low for cells expressing Piezo1 (1.2 ± 0.4 fJ; n = 39) and Piezo2 (1.0 ± 0.2 fJ; n = 47), but an order of magnitude higher for cells expressing TRAAK (21.2 ± 3.4 fJ; n = 38) and TREK1 (14.0 ±2.1 fJ; n = 60) (Fig. 3D). Analogous to our above estimate, comparing the gating energy of Piezo1 yields that even when cellular mechanotransduction is at its most sensitive, >10 5 times more energy is absorbed by the cell than is required for gating the very next ion channel. Altogether, we conclude from this analysis that detection of mechanical energy by cells, despite overexpression of FGICs, is a process that is extremely inefficient.

Molecular and Cellular Determinants of Work Threshold and
Resolution. Our above measurements of work threshold and W resolution clearly show that the specific values are dependent on the identity of the FGICs and can be quite distinct from each other. However, each specific measurement also exhibits a large degree of variability, which led us to investigate further what other molecular or cellular factors may contribute toward the cellular detection of mechanical energy. First, we reasoned that cell size could play an important role because it may determine the capacity to buffer mechanical energy. To test this idea, we took advantage of the natural variability in cell   size and correlated values for W threshold and W resolution of all individual cells with their respective electric capacitance, which scales with membrane area and is thus a proxy for cell size (45). Indeed, for both Piezo1 and Piezo2, values for W threshold are positively correlated with cell capacitance, supporting this idea (Fig. 4A). We therefore turned our attention to channel density, which we reasoned might be a more direct predictor of work threshold and W resolution because it determines the probability of activating multiple channels simultaneously. To test this idea, we performed an additional analysis taking advantage of the polymodal nature of TREK1 and TRAAK, which can be activated by both mechanical force and voltage (16,18). Specifically, we measured the membrane capacitance (C m ) as a proxy for total membrane surface area and the baseline current at 0 mV to calculate channel density in addition to probing mechanotransduction as described above ( Fig. 4B and Methods). In these measurements, channel density varied ~20-fold for TRAAK and ~50-fold for TREK1, allowing us to sample a wide range. We indeed found that values for W threshold and W resolution moderately correlate with channel density (Fig. 4 C-F). While a similar analysis is not possible for cells expressing Piezo ion channels, we found that their peak transduction currents correlate with smaller W resolution values (SI Appendix, Fig. S3).
In summary, we conclude that absolute cell size and channel density may contribute to setting the apparent threshold and resolution of cellular mechanosensing. Still, what fraction of all channels is actually activated during a given mechanical stimulus still remains unclear. Mechanotransduction differs from, for example, voltage sensing, where stimulus intensity is spatially homogeneous. In contrast, forces are generally not uniform across the entire cell (9). To answer this question, we focused on TREK1 for which we designed a new stimulation protocol. We used an internal buffer with Rb + as the dominant ion, which has been shown to left-shift the voltage dependence of TREK1 (46). In this buffer, we were able to saturate the conductance-voltage relationship of TREK1 at +160 mV and thus, after normalizing for driving force, calculate the number of channels present in the entire cell ( Fig. 4G and SI Appendix, Fig. S4). Across all cells we measured, the total number of channels ranged roughly between 1,000 and 2,000. In the same experiment, we mechanically stimulated cells, as previously described, and determined the number of channels recruited by the mechanical stimulus relative to the voltage step. Surprisingly, despite an overall large-scale compression, which elicited robust mechanically activated currents (161 ± 22 pA; n = 12), only 6.9 ± 1.2% (n = 12) of all channels were activated by this mechanical stimulus (Fig. 4H). Importantly, the value of 6.9 ± 1.2% may still be an overestimate since the mechanically gated open state of TREK1 has a two-fold higher conductance as compared to the voltage-activated state, although this was in standard K + buffer (47).
In addition, we hypothesized that the cytoskeleton, which has previously been implicated not only in mechanoprotection of FGICs but also in transmitting forces, contributes toward setting cellular detection limits (11, 22, 24-26, 48, 49). We therefore decided to disrupt the cytoskeletal architecture and measure which of these two opposing effects dominates. Specifically, we treated cells for 1 h with cytochalasin D (10 µM), which competes with barbed-end actin-binding proteins to affect both polymerization and depolymerization, destabilizing the overall actin architecture (50,51). Any reduction in W threshold or W resolution would point to a net mechanoprotective role of the actin cytoskeleton, whereas an increase would indicate mechanotransmission instead dominates. First, in separate AFM experiments we established that cytochalasin D treatment effectively reduces the elastic modulus (cells become softer): CytoD: 70.3 ± 5.7 Pa (n = 12) and untreated: 147.8 ± 20.8 Pa (n = 12), P = 0.005 ( Fig. 5 A and B). We next applied our initial AFM-electrophysiology stimulation protocol to determine W threshold and W resolution on both cytochalasin D-treated cells and day-matched vehicle controls (Fig. 5C). Cytochalasin D treatment led to a substantial decrease in the detection threshold (CytoD: 13.7 ± 1.3 fJ,    (Fig. 5D). Similarly, W resolution decreased >fourfold as compared to controls (CytoD: 0.08 ± 0.02 fJ, n = 16; DMSO: 0.38 ± 0.09 fJ, n = 14; P = 0.0073) (Fig. 5E). Surprisingly, this effect was specific to Piezo2 as we saw no significant changes in W threshold or W resolution for cells expressing TREK1, TRAAK, or Piezo1 (SI Appendix, Fig. S5), which suggests that Piezo2 is particularly sensitive to actin manipulation and that actin plays a predominantly mechanoprotective role. Taken together, we found that channel density is a general determinant of cellular sensitivity to mechanical forces and that the actin cytoskeleton is a very effective modulator of cells expressing Piezo2.
Speed of Cellular Mechanotransduction. It is known that Piezo and K2P channels open and conduct ions within milliseconds upon exposure to a mechanical stimulus (16,18,41). However, the precise timing of their response with respect to applied mechanical forces has not been quantified. In a subset of our collected recordings, we noticed a time delay (Δt) between the maximal applied force (peak force), which indicates the time point at which the piezoscanner ceases to move and compress the cell, and the resulting maximal transduction response (peak current) (Fig. 6A). Indeed, careful analysis revealed that cells expressing Piezo1, TREK1, and TRAAK exhibited a substantial response delay of 8.2 ± 2.2 ms (n = 39), 15.6 ± 2.2 ms (n = 60), and 8.5 ± 2.6 ms (n = 38), respectively. Conversely, cells expressing Piezo2 responded within 1.5 ± 0.5 ms (n = 47) (Fig. 6 B and  C). The rapid response of Piezo2 highlights that cells have, in principle, the ability to transduce forces with very fast (~1 ms) speed. Furthermore, for Piezo1 (and to a lesser extent Piezo2), the magnitude of the delay correlated with the intensity of the stimulus as measured by peak force amplitude ( Fig. 6 D and E). Importantly, we discovered that classical cell-indentation (poke) experiments on cells expressing Piezo1 also revealed a response delay, which was absent in cells expressing Piezo2, after we aligned current responses to the end of the stimulus ramp (SI Appendix, Fig. S7), giving us confidence that this phenomenon was not an artifact of our AFM instrument. We hypothesized that both channel-intrinsic and cellular properties may account for this delay. We therefore first repeated our experiments with cells expressing a chimeric channel Piezo1 cap2 , for which previous work from our laboratory demonstrated that the cap domain of Piezo2 is sufficient to confer the fast inactivation kinetics of Piezo2 onto the normally slowly inactivating Piezo1 (Fig. 6F) (42). Indeed, cells expressing Piezo1 cap2 responded within ~1 ms (1.1 ± 0.2 ms, n = 11), which is statistically identical to Piezo2 (Fig. 6G). Again, classical cell-indentation (poke) experiments produced qualitatively identical results (SI Appendix, Fig. S4). Interestingly, we found that work thresholds from the Piezo1 cap2 chimera matched those seen in Piezo2 (SI Appendix, Fig. S5). These results show that channel-intrinsic properties, and in the specific case of Piezos, the cap domain, can determine the speed of cellular mechanotransduction.
Second, membrane tension can diffuse at vastly different rates depending on cell type and local membrane properties (22,52,53). Importantly, diffusion rates are slow relative to Piezo1 activation and even inactivation. Thus, as tension diffuses through the membrane, Piezo1 ion channels may be activated at different time points, which may result in a time delay of the overall peak current relative to the stimulus (54). We therefore turned to an in silico approach to probe how the rate of tension diffusion influences the existence and magnitude of a time delay. To this end, we simulated the gating of thousands of individual, spatially randomly distributed Piezo1 channels (~100 channels/µm 2 ) with a previously validated four-state Markov model (10,54,55). We then challenged channels with a spatially confined (2 µm radius) step in membrane tension, which diffused in two dimensions with a speed of either D = 0.024 µm 2 /s, which had been determined experimentally for HeLa cells, or 10-and 100-fold faster speeds (D = 0.24 µm 2 /s and 2.4 µm 2 /s, respectively), which is still one order of magnitude below the fastest diffusion values measured in neuronal axons (D = 20 µm 2 /s) (Methods and Fig. 7 A-C) (22,53). Independent repetitions of this simulation with a diffusion constant of D = 2.4 µm 2 /s consistently showed a time delay in peak current amplitudes (dt = 6.2 ± 0.6 ms) that approximated our experimental findings for Piezo1, while simulations with slower diffusion constants (D = 0 µm 2 /s, D = 0.024 µm 2 /s, and D = 0.24 µm 2 /s) produced time delays that were less pronounced (Fig. 7E). Overall, we conclude that the time delay we observed experimentally is indeed consistent with being an emergent property of membrane tension diffusion and further that the magnitude of this time delay is determined by the identity of the FGICs and the specific diffusion rate of the cell membrane.

Discussion
In this study, we aimed to explore the capabilities and limitations of cells as transducers of mechanical energy. To this end, we developed an instrument that combines AFM with whole-cell patch-clamp electrophysiology. This approach comes with caveats and potential sources for errors that need to be considered: First, we estimate an uncertainty in cantilever calibration of ≲20%, which is consistent with other studies (56). Second, nonlinearity in the photodetector response may result in an underestimate of the most extreme forces of up to 29 ± 3% and consequently also the calculated energies. This error has only a minimal effect on work threshold values, since these are determined within the linear range of the photodetector, but may result in an overestimate of W resolution values. Third, the precise contact area between the cantilever and cell is unknown, which introduces an uncertainty in the spatial distribution of the stimulus and variability between measurements. Additionally, the time course of the stimulus (150 ms) is slow relative to the inactivation rates of the channels we studied. As a result, competing activation and inactivation lead to an underestimate of peak channel activity. Finally, by forming a whole-cell configuration, the cell is no longer a hydrostatically closed system, and mechanical load may dissipate through the patch pipette, which again may lead to an overestimate of the work performed on the cell. Indeed, this may contribute to the force relaxation we observed during the holding phase of the cantilever. In summary, the specific work values our instrument measures include not only the energy required for mechanotransduction, but also unrelated contributions, such as inelastic deformation of the cell and hydrodynamic drag on the moving cantilever. Still, the specific forces we measured at the transduction threshold for Piezo1 (228.2 ± 16.4 nN; n = 39) are comparable to those found using calcium imaging (185 nN), where the cell membrane remains intact, giving us confidence in these measurements (29). In any case, the detection threshold and W resolution we obtain for cells expressing different ion channels are clearly distinct, arguing that our instrument has sufficient precision. In addition to experimental uncertainties, our experimental preparation differs from a physiological environment in several aspects: First, we seeded cells at a low density and onto glass coverslips, which is necessary to both mechanically and electrically isolate cell properties but removes contributions from neighboring cells present in tissue and may alter the mechanical properties of the cell itself. For example, some evidence suggests that cell elasticity may vary with the stiffness of the underlying substrate, although a more recent study challenges this finding (57,58). In any case, by using glass, which has a stiffness that is much higher than that of the cantilever, substrate deformation and the related energy loss are minimized, and therefore, nearly all mechanical work is performed on the cell. Second, we overexpressed the channel of interest, which does not reflect native expression levels but is necessary to overcome potential contributions of endogenous FGICs and allowed us to clearly determine the role that channel identity plays in setting the physical limits (59,60). Third, the flat cantilever of our AFM instrument is not a natural stimulus, but the resulting large-scale compression of the cell is arguably similar to the stimulation some cell types experience in vivo: For example, chondrocytes, which express both Piezo1 and Piezo2 and form cartilage of joints, and osteoblasts, which express Piezo1 and synthesize bones, are globally compressed by body weight (6,30,59). Similarly, Merkel cells, which express Piezo2, are compressed by indentation of the skin (61). Therefore, our approach is not only biophysically useful, but to some extent also physiologically relevant. Taken together, the approach and preparation we use are not intended to match physiological settings but are ideal for exploring the limits of cell-autonomous rapid force sensing. Biological sensory systems have evolved exquisite sensitivity to their relevant stimuli, while operating under constant noise present in the environment, which ideally enables reliable detection and discrimination of relevant signals. At the lower limit, all physical systems are subject to thermal noise (k b × T = 4.11 × 10 −21 J at room temperature), and FGICs themselves are estimated to have gating energies very near to this thermal limit (10)(11)(12)(13)40). We were surprised to find that even in an overexpression system the lowest detection threshold and resolution we observed were 68.2 ± 6.3 fJ and 1.0 ± 0.2 fJ, respectively. The correlation of W resolution with peak current amplitude for cells expressing Piezo ion channels may reflect differences in expression level, or it may reflect differences in the peak amplitude of the stimulus. For comparison, our own visual system can detect single photons (~4 × 10 −19 J), although only in low-noise conditions (dark) (62). The relatively high energy required for mechanical sensing may therefore be a consequence of a high magnitude of mechanical noise present in cells, for example, caused by intrinsic forces generated by myosin motors (63). In line with this interpretation is our result that only a small fraction (6.9 ± 1.2%) of TREK1 channels is activated by our large-scale cell compression and that current responses never saturated. Our measurements clearly show that cells are inherently inefficient sensors of mechanical energies.
Three additional and very surprising findings emerged from our study: First, we found that cells can have pronounced (~10 ms) delays in their transduction response. Our chimeric approach shows that a response delay is a channel-intrinsic property and that cells can inherently respond rapidly (<1 ms). In addition, it was intriguing that this delay is almost absent in cells expressing Piezo2, which are present in DRG neurons, Merkel cells, and hair cells of the inner ear (2)(3)(4)64). It is therefore interesting to speculate that Piezo2 may have specialized to respond rapidly to fulfill its role in rapid sensory transduction. Second, our simulations show that a time delay can emerge naturally from the slow diffusion of tension. Of course, the actual spatial distribution of the stimulus and the speed of membrane diffusion that underlie our experiments are likely different from the tension clamp we simulated, which may explain the less pronounced delays in silico. Moreover, differing tension sensitivities and inactivation kinetics may explain why we found that Piezo2, TREK1, and TRAAK have response delays that are distinct from Piezo1. For example, increased tension sensitivity or slower inactivation kinetics may easily explain how channels can be activated with high probability far away from the stimulation site, altogether resulting in longer response delays. Importantly, recent work has shown that certain subcellular domains may be specialized to diffuse tension much faster, allowing long-range mechanical coupling. Interestingly, neuronal axons are among these regions which may have important implications for the transduction of mechanical touch (52,53). We propose that in addition to long-range mechanical coupling, tuning the rate of tension diffusion has important implications for the timing of the mechanotransduction response. This property may be particularly important for sensory systems, where the cellular response needs to reliably reflect the temporal characteristics of the underlying stimulus.
Third, we found that cells expressing TRAAK and TREK1 function as proportional transducers of mechanical energy, whereas cells expressing Piezos showed a highly nonlinear step-like response. Qualitatively, this behavior is reminiscent of the pressure clamp (stretch-induced) responses for TRAAK and TREK1, which have shallower slopes in their pressure response curves relative to Piezo1 (17,41,65). On a cellular level, this response property has important implications for how stimulus intensity is encoded. For example, a shallow, graded response is better suited to encode stimuli across a wider dynamic range, whereas a steep, switch-like response is better suited to encode the crossing of a particular threshold. Interestingly, Piezo1 showed a particularly steep W/I relationship, which raises the question of how this widely expressed ion channel may endow different cell types to sense distinct mechanical stimulus intensities.
We also identified several factors that influence the response properties of cells. Our data suggest that cell size and channel density may be mechanisms to modulate the response properties of cells. The fact that we only observed a correlation between cell size and response properties in cells expressing Piezos, but not K2P channels, may be due to differences in dynamic range and variability in expression levels we are able to explore. In the current study, we limited our exploration of both cell size and channel density to within the natural variation seen in transfected HEK293T cells. As a result, extreme values are underrepresented. Future studies manipulating cell geometry and FGIC expression levels can clarify the distinct contributions of each of these factors to the overall mechanotransduction response. Additionally, disrupting the cytoskeleton resulted in a stark decrease in both the detection threshold and the W resolution , specifically in cells expressing Piezo2. This result is consistent with the cytoskeleton playing a strong mechanoprotective role by limiting the transmission of mechanical energy to Piezo2 channels and also contributes to existing evidence for distinct gating mechanisms of Piezo1 and Piezo2 (66,67). It would be interesting to see, given the role of Piezo2 in sensory transduction, whether specialized sensory cells take advantage of this sensitivity to actin disruption, for instance, by localizing Piezo2 to specialized signaling domains of low actin density. Although treatment with cytochalasin D does not change work threshold values for Piezo1, TREK1, and TRAAK, the cytoskeleton may still be an important substrate for buffering mechanical energy because chemical disruption is likely incomplete. It would be interesting to explore whether other cytoskeletal elements, such as the microtubules or excess lipid reservoirs found in caveoli, contribute to a cell's ability to buffer mechanical energy (68,69).
Altogether, our approach and its results provide a quantitative framework for understanding the energetics of mechanosensing on the level of single cells. A natural extension of this work would be to next characterize primary mechanosensory cells. From there, we may learn the magnitudes of mechanical energies a particular cell type is tuned to sense, how they compare to the parameter space we found in our heterologous system, and finally what mechanisms these cells may have to extend or constrain their properties as cellular mechanosensors.
Cells were treated with cytochalasin D (10 μM solubilized in dimethyl sulfoxide (DMSO); both Sigma, Burlington, MA) for 1 h prior to and throughout the recording session. Control cells were day-matched and treated with an equal volume of DMSO over the same time course. AFM Instrument. A Digital Instruments (Bruker, Billerica, MA) BioScope was modified for simultaneous use with electrophysiology: A custom-designed aluminum stage was manufactured (Protolabs, Maple Plain, MN) to mount the BioScope to a Nikon Ti-E inverted microscope (Nikon, Tokyo, Japan). The position limiters on the stock BioScope head were removed, and a custom stopper was designed and 3D printed to increase the lower limit of the BioScope head position. The stock fluid cell probe holder was BK-7 glass with antireflective coating and custom cut (Mindrum Precision, Rancho Cucamonga, CA) to allow access to a patch pipette near the cantilever tip. The pipette manipulator was set to a 15° angle, and the stage (Nikon, Tokyo, Japan) was additionally modified to increase the lower limit of the manipulator position. A large bath was 3D printed to allow positioning of both the probe holder and a patch pipette over the coverslip. The photodetector signal was passed from the BioScope through a signal access module (Veeco, Plainview, NY) to an EPC10 amplifier (HEKA Elektronik). The signal access module also allowed external control of the piezoscanner. For this, a digital trigger signal was passed from Patchmaster (HEKA Elektronik) to custom software written in LabVIEW 2016 (National Instruments, Austin, TX) generating the stimulus waveform, which was then passed to a high-voltage amplifier (EPA-104; Piezo.com, Woburn, MA) and subsequently via the signal access module to the Nanoscope3a controller (Bruker) and the piezoscanner z-drive. The correspondence between the scanner position and the applied command voltage was determined by the scanner calibration in Nanoscope software (v5.33) after manufacturer calibration. AFM Calibration. CSC37 (length: 300 µm and width: 35 µm; used in all experiments involving channel overexpression), CSC38 (length: 300 and width: 32.5; used in cytoskeletal manipulation), or NSC35 (length: 130 µm and width: 35 µm; used in YFP overexpression) tipless, chromium-and gold-coated cantilevers (MikroMasch, Tallinn, Estonia) were mounted to a custom probe holder and attached to the BioScope head. Prior to experiments, for each individual cantilever, the stiffness was determined using the method of Sader (71)(72)(73)(74). Briefly, the dimensions of the cantilever were measured optically (Nikon Ti-E). The quality factor (Q), amplitude (A), and resonant frequency (f 0 ) were determined by fitting the equation for a simple harmonic oscillator to power spectra of the free cantilever vertical displacement signal (P) in air averaged across 512 spectra using Welch's method (75) and sampled at >fivefold the expected resonance frequency using a National Instruments Data Acquisition Board (NI-USB 6361).
The resonant frequency (f 0 ), quality factor (Q), cantilever length (L), and width (w) were used to determine the stiffness of the cantilever (k) using the following relationship: where ρ air is the density of air at 25 °C (1.18 kg/m 3 ), and Γ i (f 0 , w) is the imaginary component of the hydrodynamic function. The photodetector sensitivity was calibrated by pressing the mounted cantilever onto bare glass prior to stimulating a nearby cell and using the inverse optical lever sensitivity (invOLS) method (76,77). Briefly, due to the high stiffness of the coverslip relative to the cantilever, the slope of the relationship between the vertical difference signal of the photodetector and the piezoscanner position is defined to be 1. Thus, the inverse of the measured slope equals the sensitivity. We calculated the average sensitivity from 10 individual measurements. All sensitivity calibrations were performed in standard recording buffers prior to measuring each cell. We estimated the uncertainty in our measurements on a subset of 20 cells based on the uncertainty in the fit parameters and the variance in the sensitivity calibration to be ≲20%. In addition, we estimated the upper limit of work caused by hydrodynamic drag on the cantilever by measuring the work over a distance of 500 nm prior to cell contact and extrapolating this value over the maximal travel distance of 6 µm (11.8 ± 2.2 fJ; n = 20).
AFM Stimulation of HEK293T Cells. All stimuli were applied at 5-s intervals. Prior to initial contact, a coarse step motor moved the cantilever into contact with the cell in 1-to 5-µm steps. Contact was determined by a sudden increase in the photodetector signal. Following contact, the step motor moved the cantilever toward the cell in 0.2-to 1-µm increments until mechanotransduction currents were observed or patch rupture. Stimuli were continuously applied at a rate of 40 μm/s for a total cantilever travel distance of ~6 μm, while the cantilever was stepped downward until a mechanotransduction current was observed or the seal was disrupted. Cells expressing Piezo1 and Piezo2 were held at −80 mV during mechanical stimulation. Cells expressing TRAAK and TREK1 were held at 0 mV during mechanical stimulation to minimize current contamination from endogenous FGICs and at −80 mV between stimulus applications unless indicated otherwise.
Electrophysiology. All whole-cell recordings were performed at room temperature using an EPC10 amplifier and Patchmaster software (HEKA Elektronik). Data were sampled at 25 kHz and filtered at 2.9 kHz using an 8-pole Bessel filter. Series resistance was compensated 20 to 65%. Thin-walled borosilicate glass pipettes (1.5 mm OD and 1.17 mm ID; Sutter Instrument Company, Novato, CA) were pulled and wrapped in parafilm to reduce pipette capacitance. For TREK1 experiments using RbCl-based solutions, the bath solution consisted of (in mM) 140 NaCl, 3 MgCl 2 , 1 CaCl 2 , 10 HEPES, 30 KCl, 10 glucose, and 10 TEA-Cl. The pipette solution for these experiments consisted of (in mM) 133 RbCl, 1 MgCl 2 , 10 HEPES, 0.5 EGTA, 4 MgATP, and 0.4 Na 2 GTP. For bath solutions, pH was adjusted to 7.4 and for pipette solutions 7.2 using the hydroxide of the dominant cationic species. Osmolality was adjusted to ~310 for bath solutions and ~290 for pipette solutions with sucrose when necessary. The internal solution was allowed 3 min to dialyze prior to recording to promote GTP-mediated run-up of Piezo currents (78). Recording sessions for individual coverslips were limited to 1 h. Elasticity Measurements. Cell elasticity measurements were performed with gold-and chromium-coated cantilevers with ~10-µm borosilicate colloid probes (CP-qp-CONT-BSG: NanoandMore USA, Watsonville, CA). The exact probe diameter was measured using an FEI Apreo scanning electron microscope (SEM) and averaged from the major and minor diameters of an overlayed ellipse. The cantilever was calibrated as described above with the exception that only a single invOLS measurement was performed at the start of each measurement. The cantilever was displaced a total distance of ~6 μm at a rate of 1 µm/s before being immediately retracted at the same speed. A linear fit was performed on the first 20% of the data, prior to contact, and subtracted from the trace. The contact point was determined, based on visual inspection, as the inflection point of the force-distance curve. A Hertzian contact model was fit to the first 1 μm of the force-distance curve following the contact point and used to estimate the elastic modulus (E) as follows: where R is the radius of the probe determined by scanning electron microscope imaging, υ is the Poisson ratio taken to be 0.5, and δ is the indentation depth.
Analysis. All data were analyzed using custom analyses written in R, Python, and Julia (GitHub: GrandlLab) (79). Cells with leak currents >300 pA at −80 mV or series resistances >15 MΩ were excluded from the analysis. Cells were determined to be responsive to mechanical stimuli if they displayed stimulus-locked whole-cell currents of 50 pA prior to patch rupture. Baseline currents and photodetector voltage in the absence of mechanical stimulation were subtracted offline. For TRAAK and TREK1, the mechanocurrent was isolated from the voltage-dependent current by subtracting the current amplitude at 0 mV. The compression force (F) was calculated from the baseline subtracted vertical difference signal of the photodetector (V PD ) using the following equation, where S denotes the sensitivity, and k cant denotes the cantilever stiffness: The distance traveled by the cantilever was corrected to account for cantilever deflection using the following equation: where α is the calibration factor for the piezoscanner, V command is the command voltage sent to the photodetector, and δ is the deflection of the cantilever. The work was determined by calculating the cumulative integral of the calculated force as a function of the distance traveled by the cantilever.
For analyses of the approach phase of each stimulus, only data during the initial ramp of the cantilever were considered.
Transduction characteristics were determined as follows: 1) Power coefficients for individual W/I curves were determined by removing data prior to the work threshold, log transforming, and performing a linear fit. 2) Work threshold (Wthreshold) values were determined as the maximum work, at which the current remains below 2 SDs above the baseline current as follows: where the SD was calculated over a 100-ms window preceding stimulus onset.
The average values for 2 SD were 4.0 ± 0.5 pA for Piezo1, 4.4 ± 0.4 pA for Piezo2, 7.5 ± 0.7 pA for TRAAK, and 12.8 ± 0.8 pA for TREK1. Current threshold values for TREK1 and TRAAK are likely slightly higher due to their higher open probability at 0 mV. Current traces were passed through an additional 6-pole Bessel filter with a cutoff frequency of 1 kHz offline prior to threshold determination. 3) W resolution values were calculated from the inverse slope (dW/dI) by performing a linear least square fit to the range of data corresponding to the steepest region of the W/I relationship and the following equation: using previously reported single-channel conductances (g C ) (Piezo1: 29.1 pS, Piezo2: 23.7 pS (44), TRAAK: 65.4 pS, and TREK1: 88.5 pS (43)). The reversal potential (E R ) was estimated to be 0 mV for Piezo channels and the Nernst potential for potassium (−95 mV) in the solutions used for K2P channels. 4) Channel density was estimated using the mean current (Iv) at 0 mV in the absence of a mechanical stimulus and the C m using the following equation: where g c is the respective single-channel current at the applied voltage, and C S is the approximate capacitivity of biological membranes of 1 µF/cm 2 (80). 5) The total number (N) of TREK1 channels was calculated using the following equation: where I 160 is the current at 160 mV, I Leak is the current obtained from a post hoc linear fit to currents evoked by increasing negative steps from −80 mV to −90 mV to −80 to −120 mV, g Trek1 the unitary conductance for TREK1 in K + buffers (43), and E R the reversal potential in Rb + buffer determined with a tail current protocol (SI Appendix, Fig. S2).
6) The number of channels activated by a mechanical stimulus (Nmech) was calculated by additionally subtracting the voltage-activated current (I 0 ) at 0 mV from the mechanically activated current (Imech) and using the following equation: 7) The response delay (Δt) in AFM experiments was calculated as the time difference between the peak of the mechanically activated current t peak current and the peak of the applied force t peak Force as follows: 8) The response delay (Δt) in traditional poke experiments was calculated as the time difference between the peak of the mechanically activated current t peak current and the peak of the stimulus ramp t peak Stimulus as follows: Stimulus . All values reported are bootstrapped means ± SEM unless otherwise noted. All statistical analyses were performed using Welch's t test for two group comparisons. For omnibus tests, Welch's ANOVA was performed followed by a post hoc Games-Howell test. Significance thresholds correspond to *P < 0.05, **P < 0.005, and ***P < 0.001. Bootstrap distributions and CIs were determined using the bias-corrected and accelerated bootstrapping method except where SEM is reported in which case percentile bootstrap distributions were used. All bootstrapping was done with ≥10,000 replicates.

Markov Model Simulations.
Channel gating was simulated with a custom-written script using Python available on GitHub (GitHub: GrandlLab) (81). Piezo1 channels were distributed randomly on a grid with 10 nm × 10 nm pixel size. The grid size was adjusted for each simulation to minimize simulation time and to ensure tension at the edge never exceeded 5% of the maximal tension amplitude to minimize boundary effects. Pixel occupancy was approximately 1% corresponding to the experimentally obtained channel density of Piezo1 overexpressed in Neuro2A cells of 100 channels/μm 2 (55). Gating of each individual Piezo1 channel was simulated with a four-state Markov model (Fig. 7C) as previously described and adapted to be a function of membrane tension (σ) (9,10,54). Specifically, rate constants for wild-type Piezo1 (σ 50 = 1.4 mN/m and slope factor b = 0.8 mN/m) were k 1 (σ) = 5.1 × exp(σ/b) s −1 , k -1 = 5 × exp(σ 50 /b) s −1 , k 2 = 8.0 s −1 , k -2 = 0.4 s −1 , k 3 (σ) = 34.6 × exp(−σ/b) s −1 , k 4 = 4.0 s −1 , k -4 = 0.6 s −1 , where σ is the applied tension, and k -3 = (k 1 × k 2 × k 3 )/(k -1 × k -2 ) to achieve microscopic reversibility. Sampling intervals (dt) were adjusted such that dt << 1/k 1 (σ) at all times and ranged from 0.1 to 10 μs. Equilibrium occupancies at σ = 0 were determined analytically and used as starting values. Each simulation was allowed an additional 50 ms at σ = 0 to ensure complete equilibration before the tension stimulus was applied. At t = 50 ms, a circular tension stimulus with radius = 4 μm (200 pixels) was applied. Propagation of membrane tension was calculated with a 2D Gaussian diffusion function (Fig. 7B) as follows: where σ max is the maximal tension amplitude, D the diffusion coefficient, r is the distance of the channel from the edge of the stimulus, and t is the time after stimulus onset. Initially, 1-s simulations were performed to validate the baseline current, peak current, inactivation kinetics, plateau current matched expected values. Shorter simulations (90 ms) were produced to calculate response delay as a function of diffusion coefficient. Delay times were calculated by determining the time poststimulus onset, at which the maximum number of opened channels occurred. Stimulations were repeated 10 times for each condition. All data are mean + SEM.
Data, Materials, and Software Availability. All code associated with cantilever calibration, photodetector calibration, data analysis, and simulation are available and accompanied by reproducible environments and documentation on the laboratory GitHub page (74,77,79,81). Source data files have been provided with the numerical data for each figure. Raw data are hosted on Dryad and can be accessed at https://doi.org/10.5061/dryad.gtht76hq5 (82).
ACKNOWLEDGMENTS. This study was supported by the NIH 5R01NS110552 (M.N.Y. and J.G), The Ruth K. Broad Biomedical Research Foundation (M.N.Y.), and the Duke Institute for Brain Sciences (DIBS). We thank Marie Cronin for thoughtful comments on the study and Tejank Shah for technical assistance.